When she is older, two-year-old Nell Burton may view her father's film of Alice in Wonderland with a particularly curious eye. For her mother, Helena Bonham Carter, last night revealed that she based her tyrannical Red Queen on her and Tim Burton's young daughter.

While the toddler is presumably not given to ordering the beheadings of those who surround her, Bonham Carter said Nell was the main inspiration for the bossy, spiteful monarch who maintains a reign of terror over Wonderland in Burton's 3D CGI reimagining.

"I thought: well, she's a toddler, because she's got the big head," Bonham Carter revealed at a press conference ahead of last night's London premiere. "She's a tyrant … toddlers are tyrants. The 'no sympathy for any other living creature' – that's our toddler, in fact.

"[There's] no empathy, just commands. She just bosses us around – dictatorship. No please, no thank you. 'Mummy come here', 'Mummy go', 'Mummy! Watch telly'.

"And another toddler quality – it's all about me, it's all about her, never considers us: ask, ask, ask. So the toddler thing was a big inspiration."

Johnny Depp plays the Mad Hatter, guide and mentor to Alice, who in Burton's version is a 19-year-old returning to Wonderland after many years away. The Oscar-nominated actor said the character's look and manner were inspired by his own research into 19th-century London hat makers.

"I discovered that they used this very toxic substance to glue the hats together, which involved a lot of mercury and ended up poisoning them heavily," he said. "The way it manifested itself was often in Tourette's-like symptoms or personality disorders.

"It was about extreme personalities, so one minute you're at full capacity rage, then it's a horrific tailspin of fear and next a great height of levity. There was an orange tint to the special stuff, so that's where all the orange bits came from," he added.

Early reviews of Alice in Wonderland have been broadly positive, with the Guardian's Xan Brooks calling it "a film in which the art direction eats the magic cake and swells to giant proportions", although he does add: "The script drinks from the magic vial and shrinks away to insignificance."

This ought to release some of the pressure on Burton – the $250m (£164m) project is his first to be released under the Disney banner. Yet the film-maker said he had not approached the film with any fear, despite its well-loved subject.

"I just loved the trippiness of the story," he said. "There's been over 20-some versions of it and it is so much a part of our culture, through music and bands and other artists' interpretations, but for me, it felt like it was open territory because there hasn't really been a definitive version."